E6 AND THE ARITHMETIC OF A FAMILY OF NON-HYPERELLIPTIC CURVES OF GENUS 3
Published version
Peer-reviewed
Repository URI
Repository DOI
Change log
Authors
THORNE, JACKA
Abstract
We study the arithmetic of a family of non-hyperelliptic curves of genus 3 over the field Q of rational numbers. These curves are the nearby fibers of the semi-universal deformation of a simple singularity of type E6 . We show that average size of the 2-Selmer sets of these curves is finite (if it exists). We use this to show that a positive proposition of these curves (when ordered by height) has integral points everywhere locally, but no integral points globally.
Description
Keywords
4903 Numerical and Computational Mathematics, 4904 Pure Mathematics, 49 Mathematical Sciences
Journal Title
Forum of Mathematics, Pi
Conference Name
Journal ISSN
2050-5086
2050-5086
2050-5086
Volume Title
3
Publisher
Cambridge University Press (CUP)
Publisher DOI
Sponsorship
Engineering and Physical Sciences Research Council (EP/N007204/1)